Probability

Inductive Reasoning

Instead, a correct solution is achieved by applying a normatively appropriate rule f inference. Normative systems are often applied to formal reasoning problems in order to define solutions as right or wrong, such that these problems are then construed as tests f correct and fallacious reasoning. Hence, these problems are designed to measure the extent to which participants bring to the laboratory an understanding – and ability to apply – the relative normative principles.
In the case f deductive reasoning research, the relevant normative system is formal logic. Participants are given some premises and asked whether a conclusion follows. Under strict deductive reasoning instructions, they are told (a) to assume that the premises are true and (b) to draw or approve only conclusions that necessarily follow. As observed elsewhere (Evans, 2002), this widely used method was developed over 40 years ago when belief in logic as a normative and descriptive system for human reasoning was very much higher than it is today. In spite f the method, much evidence has emerged to support the conclusion that pragmatic factors play a large part in human reasoning. We say "in spite of" because standard deductive instructions aim to suppress precisely those factors that dominate informal reasoning: the introduction f prior belief and the expression f uncertainty in premises and conclusions.
In research on statistical inference, a similar story is found. People are asked to make statistical inference on the basis f well-defined problems, in which relevant probabilities or frequency distributions are provided, and their answers are assessed for correctness against the norms provided by the probability calculus. Research in this tradition has been mostly conducted by researchers in the "heuristics and biases" tradition inspired by the work f Danny Kahneman and Amos Tversky (Gilovich, Griffin, &amp. Kahneman, 2002. Kahneman, Slovic, &amp. Tversky, 1982). This results in an arguably negative research strategy that is similar to much work on deductive reasoning. That is, researchers show primarily what people cannot do (conform to the principles f logic or probability theory) and only secondarily address what people actually do.
Indeed, one f the most common explanations for why intelligent, educated individuals often fail to reason normatively is that they use informal reasoning processes to solve formal reasoning tasks. For example, notwithstanding instructions to the contrary, reasoners often supplement the information they are provided with background knowledge and beliefs, and make inferences that are consistent with, rather than necessitated by, the premises. If this is the case, it is reasonable to suggest that we study these processes directly, by giving our participants tasks that allow them to express these types f behaviours freely, rather than indirectly, via the observation f poor performance on a formal task. (Vallee-Tournageau 2005)
The argument for doing so becomes even more compelling when it is understood that performance on any given reasoning task

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